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So long from ECONOMICS E- 1010 : MICROECONOMIC THEORY

So long from ECONOMICS E- 1010 : MICROECONOMIC THEORY. Fall 2011 W, 5:30-7:30 Maxwell Dworkin , G115 Robert Neugeboren 51 Brattle St, Rm 523 TA: Rajiv Shankar W 3-4 and by app ’ t. rshankar@fas.harvard.edu

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So long from ECONOMICS E- 1010 : MICROECONOMIC THEORY

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  1. So long from ECONOMICSE-1010:MICROECONOMIC THEORY Fall 2011 W, 5:30-7:30 Maxwell Dworkin, G115 Robert Neugeboren 51 Brattle St, Rm 523 TA: Rajiv Shankar W 3-4 and by app’t.rshankar@fas.harvard.edu neugebor@fas.harvard.edu Sections: Th 5:30-6:30 Website: www.isites.harvard.edu/k82088 \

  2. IMPORTANT Exam Room Change SCIENCE CENTER C 12/14/2011 5:30pm

  3. Today’s Agenda • Course Overview • Exam Structure • Closing Remarks Tomorrow: Problem Set Review (R. Shankar)

  4. Course Overview UNIT I CONSUMER CHOICE UNIT IIFIRM BEHAVIOR Oct 19 MIDTERM UNIT III MARKETS & COMPETITIVE STRATEGY UNIT IV INFORMATION & WELFARE Dec 14FINAL EXAM

  5. Course Overview UNIT I CONSUMER CHOICE: Optimization under constraint Income and substitution effects Consumer demand UNIT IIFIRM BEHAVIOR: Cost minimization Profit maximization Perfect Competition Welfare analysis MIDTERM

  6. Optimization We assume that a rational consumer will attempt to maximize her utility. But utility increases with consumption of all goods, so utility functions have no maximum -- more is always better! Y X Indifference Curves depict consumer’s “willingness to trade” Indifference Curves depict consumer’s “willingness to trade” Slope = - MRS DY DX

  7. Optimization We assume that a rational consumer will attempt to maximize her utility. But utility increases with consumption of all goods, so utility functions have no maximum -- more is always better! Y X Indifference Curves depict consumer’s “willingness to trade” Indifference Curves depict consumer’s “willingness to trade” Slope = - MRS Budget Constraint depicts “opportunities to trade” Slope = - Px/Py A B At point A, MRS > Px/Py, so consumer should trade Y for X.

  8. Optimization The optimal consumption bundle places the consumer on the highest feasible indifference curve, given her preferences and the opportunities to trade (her income & the prices she faces). Y Y* X* X Indifference Curvesdepict consumer’s “willingness to trade” Slope = - MRS Budget Constraint depicts “opportunities to trade” Slope = - Px/Py C At point C, MRS = Px/Py, so consumer can’t improve thru trade.

  9. Optimization Two Conditions for Optimization under Constraint: 1. PxX + PyY = I Spend entire budget 2. MRSyx = Px/PyTangency MRSyx = MUx/MUy = Px/Py => MUx/Px = MUy/Py The marginal utility of the last dollar spent on each good should be the same.

  10. Optimization: An Example Pat divides a monthly income of $1800 between consumption of food (X) and consumption of all other goods (Y). Pat’s preferences can be described by the following utility function: U = X2Y If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle. Pat should choose the combination of food and all other goods that places her on the highest feasible indifference curve, given her income and the prices she faces. This is the point where an indifference curve is tangent to the budget constraint (unless there is a comer solution).

  11. Optimization: An Example Graphically: Y X Maximize: U = X2Y Subject to: I = PxX + PyY I = 1800; Py = $2; Px= $1 Y* = 300, X* = 1200. 900 Y*=300 X*=1200

  12. Optimization: An Example Graphically: Y X Maximize: U = X2Y Subject to: I = PxX + PyY I = 1800; Py = $2;Px’ = $2 Y** = 300, X** = 600. Now suppose the price of food rises to $2 900 Y**=300 X**= 600 1200

  13. Income & Substitution Effects Y X The change in price affects consumption via 2 causal channels: Because the relative price of food has increased, Pat will consume less food (and more of all other goods). This the substitution effect. 900 Y**=300 S X**= 600 1200 S

  14. Income & Substitution Effects Y X But because Pat is now relatively poorer (her purchasing power has decreased), she will consume less of both goods.This is the income effect. In this case, the 2 effects are equal and opposite for Y, additive for X. The change in price affects consumption via 2 causal channels: 900 Y**=300 X**= 600 1200

  15. Consumer Demand U = X2Y I = 1800; Py = 2 Y X Px Y X $1 300 1200 2 300 600 3 300 400 900 Y***=300 X***=400

  16. Consumer Demand U = X2Y I = 1800; Py = 2 MUx = 2XY; MUy = X2 MRS = 2Y/X = Px/Py = Px/2 => Y = (1/4)PxX I = PxX + PyY 1800 = PxX + (2)(1/4)PxX = (3/2)PxX X = 1200/Px Demand Curve X = f(Px) 1200 1 600 2 400 3 Y Px Solve for Y & substitute 3 2 1 X X Px = 3 2 1 400 600 1200

  17. Course Overview UNIT I CONSUMER CHOICE: Optimization under constraint Income and substitution effects Consumer demand UNIT IIFIRM BEHAVIOR: Cost minimization Profit maximization Perfect Competition Welfare analysis MIDTERM • X* = f(Px) • Q* = f(P)

  18. Theory of the Firm Our basic model assumes the firm seeks to maximize: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate Q = f(K,L) r Rate on Capital INPUTS The production functiondescribes a relationship between the quantity of physical inputs (K, L) and quantity of outputs (Q).

  19. Theory of the Firm First, we need to write down our model: Profit (P) = Total Revenue(TR) – Total Cost(TC) TR(Q) = PQ TC(Q) = rK + wL P Price L Labor Q Quantity K Capital w Wage Rate Q = f(K,L) r Rate on Capital OUTPUT The production functiondescribes a relationship between the quantity of physical inputs (K, L) and quantity of output (Q).

  20. Cost Minimization in the Long-Run How much will it cost this firm to produce Q units of output in the long-run? An isoquant is all the technologically efficient combinations of K ,L to produce a certain output, Q. K Isoquant Slope = - MRTS Q L

  21. Cost Minimization in the Long-Run How much will it cost this firm to produce Qunits of output in the long-run? If we think of the allthe combinations of K&L that cost a certain amount (TC), we have anisocost line: K = TC/r – (w/r)L Recall: TC = wL + rK K Isocost lines Slope = - w/r Q L

  22. Cost Minimization in the Long-Run How much will it cost this firm to produce Q units of output in the long-run? Tangency between the isoquant and an isocost curve shows the economically efficient combination K*, L*. Hence, the condition for optimal factor proportion is: MRTS = w/r K K* Isocost lines Slope = - w/r Isoquant Slope = - MRTS Q L* L

  23. Cost Minimization in the Long-Run How much will it cost this firm to produce Q units of output in the long-run? The condition for optimal factor proportion is: MRTS = w/r This is LR condition!Why? Because some factors (K) are fixed in the SR. K K* Isocost lines Slope = - w/r Isoquant Slope = - MRTS Q L* L

  24. Cost Minimization: Summary We can solve the firm’s cost minimization problem analogously to the consumer’s utility maximization problem. Cost minimization requires that the firm produce using a combination of inputs for which the ratios of the marginal products, or the marginal rate of technical substitution, equals the ratio of the input prices: MRTS = w/r • 2 Provisos: • Only in the Long-Run • Only part of the firm’s problem

  25. Profit Maximization The firm wants tomaximize this difference: Profit (P) = Total Revenue(TR) – Total Cost(TC) $ To maximize profits, the firm finds Q where distance between TC and TR is greatest. This will be where they have the same slope. TR = PQ Pmax TC Q* Q

  26. Profit Maximization Marginal Analysis: Recall: slope TR = MR slope TC = MC Hence, to maximize profits: MR = MC Profit (P) = Total Revenue(TR) – Total Cost(TC) $ TR = PQ Pmax TC Q* Q

  27. Profit Maximization Consider a firm that produces output according to the following production function. Q = 4K1/2L1/2 w = 18; r = 36 MRTS = MPL/MPK MPL = 2K1/2L-1/2 MPK = 2K-1/2L1/2 MRTS = K/L. = w/r = 18/36 = L = 2K. The firm’s optimal factor proportion (given technology and factor prices).

  28. Profit Maximization Consider a firm that produces output according to the following production function. Q = 4K1/2L1/2 w = 18; r = 36 TC = TC(Q) = rK + wL = 18L + 36K = 9Q/(2)1/2 + 9Q/(2)1/2 = 18/(2)1/2(Q) TC = 12.73Q MC = 12.73

  29. Profit Maximization Demand for the firm’s output is given by Q = 100 – 2P. Find the firm’s profit maximizing level of output. Q = 4K1/2L1/2 w = 18; r = 36 Q = 100 – 2P => P = 50 – 1/2Q TR = PQ = (50 – 1/2Q)Q = 50Q – 1/2 Q2 MR = 50 – Q = MC = 12.73 => Q* = 37.27; P* = 31.37

  30. Profit Maximization Demand for the firm’s output is given by Q = 100 – 2P. Find the firm’s profit maximizing level of output. Q = 4K1/2L1/2 w = 18; r = 36 Q = 100 – 2P => P = 50 – 1/2Q TR = PQ = (50 – 1/2Q)Q P = TR – TC = 50Q – 1/2 Q2 – 12.73Q FOC: dP/dQ = 50 – Q – 12.73 = 0 => Q* = 37.27; P* = 31.37

  31. Profit Maximization We saw that the firm maximizes profit by choosing a level of output such that marginal revenue equals marginal cost MR = MC. In the long-run, this implies that the firm will be utilizing its optimal factor proportion, such that MRTS = w/r. In the short-run, the firm’s profit maximizing calculus weighs the benefit of hiring an additional unit of labor versus its cost. If the firm can add (subtract) another unit of labor and increase revenue by more than it increases cost, it should add (subtract) it, and it should keep on adding (subtracting) until MR = MC.

  32. Profit Maximization in the Short-Run So the firm’s short-run optimality condition can be rewritten as: MRPL = MFCL If the firm can add (subtract) another unit of labor and increase revenue by more than it increases cost, it should add (subtract) it, and it should keep on adding (subtracting) until MRPL = MFCL. This, in turn, is what determines the firm’s (short-run) demand for labor: P (MPL) = w

  33. Perfect Competition Assumptions • Firms are price-takers: can sell all the output they want at P*; can sell nothing at any price > P*. • Homogenous product: e.g., wheat, t-shirts, long-distance phone minutes. • Perfect factor mobility: in the long run, factors can move costlessly to where they are most productive (highest w, r). • Perfect information: firms know everything about costs, consumer demand, other profitable opportunities, etc.

  34. Perfect Competition The Short-run & the Long-run In the short-run, firms adjust to price signals by varying their utilization of labor (variable factors). In the long-run, firms adjust to profit signals by • varying plant size (fixed factors); and • entering or exiting the market. We can use this story to understand (and solve for) the long-run competitive equilibrium. P = 0 P = 0

  35. Perfect Competition Short-run equilibrium with three firms. Firm A is making positive profits, Firm B is making zero profits, and Firm C is making negative profits (losses). q: firm Q: market mc mc $ P mc ac ac ac qa* qb* qc* Firm A Firm B Firm C

  36. Perfect Competition In the long-run, if there are no barriers to entry, then new firms have access to the most efficient productiontechnology. We call this the efficient scale. $ P* mc mc mc ac ac ac q* q q* q q* q Firm A Firm D Firm E

  37. Perfect Competition Long-run equilibrium. Firms are producing at the efficient scale. P* = ACmin; P = 0. $ $ P* mc ac LRS D q* q Q* Q

  38. Perfect Competition In the Long-run… • Firms produce at minimum average cost, i.e., “efficient scale.” (AC = ACmin) • Price is equal to marginal cost. (P = MC) • Firms earn zero (economic) profits. (p = 0) • Market equilibrium is Pareto-efficient.

  39. Perfect Competition Consider a perfectly competitive industry characterized by the following total cost and demand functions: TC = 100 + q2 QD = 1000 – 20P Find the market equilibrium in the long-run. How many firms are in the market?

  40. Perfect Competition tc = 100 + q2QD = 1000 – 20P 1) Firms produce at acmin i) ac = mc 100/q + q = 2q 100 + q2 = 2q2 q2 = 100; q* = 10 ii)ac’= 0 -100/q2 + 1 = 0 q2 = 100; q* = 10 $ mc = 2q $ ac = 100/q + q avc = q LRS q* is the efficient scale q* = 10 q 600 Q

  41. Perfect Competition tc = 100 + q2 QD’ = 1500 – 20P q.n = (mc/2)n = (P/2)n => QS = 30P SRS $ mc = 2q $ P* = 20 ac = 100/q + q SRS P’ = 30 avc = q LRS D’ D n = 60 q’ = 15 q Q’ = 900 Q

  42. Perfect Competition tc = 100 + q2 QD’ = 1500 – 20P $ mc = 2q $ P* = 20 ac = 100/q + q avc = q LRS D’ D n = 110 q* = 10 q Q** = 1100 Q

  43. Perfect Competition In the Long-run … • Firms produce at minimum average cost, i.e., “efficient scale.” • Price is equal to marginal cost. • Firms earn zero (economic) profits. • Market equilibrium is Pareto-efficient. Welfare analysis

  44. Equilibrium & Efficiency Is it true that the rational pursuit of private interests produces coherence rather than chaos, and if so, how is it done? -- Frank Hahn Equilibrium: most generally, an equilibrium is a state of the market in which decision plans are mutually consistent and therefore can be implemented. In the market, coordination takes place via prices: at a given price, all the output firms want to produce can be sold and all the goods consumers want to purchase can be bought.

  45. Equilibrium & Efficiency Pareto Efficiency: an economic situation is Pareto efficient if no one can be made any better off without making someone else worse off. Pareto efficiency is a “good” thing, but it says nothing about equity; income distribution; economic justice. Competitive markets produce Pareto efficient equilibria (Q*), because at Q* the price someone is willing to pay for an additional unit of the good is equal to the price that someone must be paid to sell that unit.

  46. Welfare Consumption Efficiency: All consumers are optimizing at given output prices (Px/Py) MRS1 = MRS2 Production Efficiency: All firms are optimizing (minimizing cost) at given factor prices (w/r) MRTSx = MRTSy Allocation Efficiency: Product mix will be optimal; relative prices fully reflect relative costs MRSyx = MRTyx (where MRTyx = MCx/MCy)

  47. Welfare First Theorem of Welfare Economics: All competitive equilibria are Pareto-efficient. Second Theorem of Welfare Economics: Any allocation (of wealth or goods) can be sustained in a competitive equilibrium.

  48. Course Overview UNIT III MARKETS & COMPETITIVE STRATEGY Monopoly and market power Duopoly and imperfect information Cooperation and collusion UNIT IV INFORMATION & WELFARE Risk and insurance Externalities and public goods Dec 14 FINAL EXAM

  49. Markets Imperfections • Monopoly and Market Power • Duopoly and Imperfect Information • Incomplete and Asymmetric Information • Externalities • Public Goods

  50. Market Structure Once we move away from perfect competition, firms can exploit market power: their behavior can influence prices (and profits). Monopoly is the case where a single firm has market power. Imperfect competition refers to situations in which several firms “share” power in the market (oligopoly). In such caes, firms form expections about one anothers’ behavior. Here, competitive strategy comes to the fore.

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